diff --git a/projects/README b/projects/README index 2800f85..16e9758 100644 --- a/projects/README +++ b/projects/README @@ -42,6 +42,7 @@ no statistics 9) project_mutualinfo OK, medium +Example code is missing 10) project_noiseficurves OK, simple-medium diff --git a/projects/project_ficurves/ficurves.tex b/projects/project_ficurves/ficurves.tex index b3bad65..8af5861 100644 --- a/projects/project_ficurves/ficurves.tex +++ b/projects/project_ficurves/ficurves.tex @@ -1,9 +1,9 @@ \documentclass[a4paper,12pt,pdftex]{exam} -\newcommand{\ptitle}{F-I curves} +\newcommand{\ptitle}{f-I curves} \input{../header.tex} -\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}% -{email: jan.grewe@uni-tuebingen.de} +\firstpagefooter{Supervisor: Jan Benda}{phone: 29 74573}% +{email: jan.benda@uni-tuebingen.de} \begin{document} @@ -11,64 +11,69 @@ %%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%% -\section{Quantifying the responsiveness of a neuron using the F-I curve} -The responsiveness of a neuron is often quantified using an F-I -curve. The F-I curve plots the \textbf{F}iring rate of the neuron as a -function of the stimulus \textbf{I}ntensity. - - In the accompanying datasets you find the \textit{spike\_times} of an - P-unit electroreceptor of the weakly electric fish - \textit{Apteronotus leptorhynchus} to a stimulus of a certain - intensity, i.e. the \textit{contrast}. The spike times are given in - milliseconds relative to the stimulus onset. +\section{Quantifying the responsiveness of a neuron using the f-I + curve} +The responsiveness of a neuron is often quantified using an $f$-$I$ +curve. The $f$-$I$ curve plots the \textbf{f}iring rate of the neuron +as a function of the stimulus \textbf{I}ntensity. + +In the accompanying datasets you find the \textit{spike\_times} of an +P-unit electroreceptor of the weakly electric fish \textit{Apteronotus + leptorhynchus} to a stimulus of a certain intensity, i.e. the +\textit{contrast}. The spike times are given in milliseconds relative +to the stimulus onset. \begin{questions} - \question{Estimate the FI-curce for the onset and the steady state response.} + \question Estimate the $f$-$I$-curve for the onset and the steady + state response. \begin{parts} \part Estimate for each stimulus intensity the average response - (PSTH) and plot it. You will see that there are three parts. (i) + (PSTH) and plot it. You will see that there are three parts: (i) The first 200\,ms is the baseline (no stimulus) activity. (ii) During the next 1000\,ms the stimulus was switched on. (iii) After stimulus offset the neuronal activity was recorded for further 825\,ms. - \part Extract the neuron's activity in a 50\,ms time window immediately - after stimulus onset (onset response) and 50\,ms before stimulus offset (steady state response). + \part Extract the neuron's activity in 50\,ms time windows before + stimulus onset (baseline activity), immediately after stimulus + onset (onset response), and 50\,ms before stimulus offset (steady + state response). - For each plot the resulting F-I curve by plotting the - computed firing rates against the corresponding stimulus - intensity, respectively the contrast. + Plot the resulting $f$-$I$ curves by plotting the three computed + firing rates against the corresponding stimulus intensities + (contrasts). \end{parts} - \question{} Fit a Boltzmann function to each of the F-I-curves. The - Boltzmann function is a sigmoidal function and is defined as - \begin{equation} - f(x) = \frac{\alpha-\beta}{1+e^{-k(x-x_0)}}+\beta \; . - \end{equation} - $x$ is the stimulus intensity, $\alpha$ is the starting - firing rate, $\beta$ the saturation firing rate, $x_0$ defines the - position of the sigmoid, and $k$ (together with $\alpha-\beta$) - sets the slope. - - \begin{parts} - \part{} Before you do the fitting, familiarize yourself with the four - parameters of the Boltzmann function. What is its value for very - large or very small stimulus intensities? How does the Boltzmann - function change if you change the parameters? - - \part{} Can you get good initial estimates for the parameters? - \part{} Do the fits and show the resulting Boltzmann functions together - with the corresponding data. - - \part{} Illustrate how fit to the F-I curves changes during the fitting - process. You can plot the parameters as a function fit iterations. - Which parameter stay the same, which ones change with time? - - Support your conclusion with appropriate statistical tests. - - \part{} Discuss you results with respect to encoding of different - stimulus intensities. + \question Fit a Boltzmann function to each of the $$-$I$-curves. The + Boltzmann function is a sigmoidal function and is defined as + \begin{equation} + f(x) = \frac{\alpha-\beta}{1+e^{-k(x-x_0)}}+\beta \; . + \end{equation} + $x$ is the stimulus intensity, $\alpha$ is the starting firing rate, + $\beta$ the saturation firing rate, $x_0$ defines the position of + the sigmoid, and $k$ (together with $\alpha-\beta$) sets the slope. + + \begin{parts} + \part Before you do the fitting, familiarize yourself with the + four parameters of the Boltzmann function. What is its value for + very large or very small stimulus intensities? How does the + Boltzmann function change if you change the parameters? + + \part Can you get good initial estimates for the parameters? + + \part Do the fits and show the resulting Boltzmann functions + together with the corresponding data. + + \part Illustrate how the fit to the $f$-$I$ curves changes during + the fitting process. You can plot the parameters as a function of + fit iterations. Which parameter stay the same, which ones change + with time? + + Support your conclusion with appropriate statistical tests. + + \part Discuss you results with respect to encoding of different + stimulus intensities. \end{parts} \end{questions} diff --git a/projects/project_lif/lif.tex b/projects/project_lif/lif.tex index 068b85e..343683c 100644 --- a/projects/project_lif/lif.tex +++ b/projects/project_lif/lif.tex @@ -52,7 +52,6 @@ time = [0.0:dt:tmax]; % t_i Vary the time step $\Delta t$ by factors of 10 and discuss accuracy of numerical solutions. What is a good time step? - Why is $V=0$ the resting potential of this neuron? \part Response of the passive membrane to a step input. @@ -72,15 +71,15 @@ time = [0.0:dt:tmax]; % t_i What do you observe? - \part Transfer function of the passive neuron. + \part Filter function of the passive neuron. Measure the amplitude of the voltage responses evoked by the sinusoidal inputs as the maximum of the last 900\,ms of the responses. Plot the amplitude of the response as a function of - input frequency. This is the transfer function of the passive neuron. + input frequency. This is the filter function of the passive + neuron. - How does the transfer function depend on the membrane time - constant? + How does the filter function depend on the membrane time constant? \part Leaky integrate-and-fire neuron. diff --git a/projects/project_noiseficurves/noiseficurves.tex b/projects/project_noiseficurves/noiseficurves.tex index 98f0aad..3baa199 100644 --- a/projects/project_noiseficurves/noiseficurves.tex +++ b/projects/project_noiseficurves/noiseficurves.tex @@ -54,10 +54,10 @@ spikes = lifspikes(trials, current, tmax, Dnoise); \begin{parts} \part First set the noise \texttt{Dnoise=0} (no noise). Compute - and plot neuron's $f$-$I$ curve, i.e. the mean firing rate (number - of spikes within the recording time \texttt{tmax} divided by - \texttt{tmax} and averaged over trials) as a function of the input - current for inputs ranging from 0 to 20. + and plot the neuron's $f$-$I$ curve, i.e. the mean firing rate + (number of spikes within the recording time \texttt{tmax} divided + by \texttt{tmax} and averaged over trials) as a function of the + input current for inputs ranging from 0 to 20. How are different stimulus intensities encoded by the firing rate of this neuron? diff --git a/projects/project_populationvector/populationvector.tex b/projects/project_populationvector/populationvector.tex index d16bdaa..ee40c66 100644 --- a/projects/project_populationvector/populationvector.tex +++ b/projects/project_populationvector/populationvector.tex @@ -39,7 +39,7 @@ \begin{parts} \part Illustrate the spiking activity of the V1 cells in response to different orientation angles of the bars by means of spike - raster plots (of one unit). + raster plots (of a single unit). \part Plot the firing rate of each of the 6 neurons as a function of the orientation angle of the bar. As the firing rate compute @@ -48,7 +48,7 @@ of the neurons. \part Fit the function \[ r(\varphi) = - g(1+\cos(\varphi-\varphi_0))/2 \] to the measured tuning curves in + g(1+\cos(2(\varphi-\varphi_0)))/2 \] to the measured tuning curves in order to estimated the orientation angle at which the neurons respond strongest. In this function $\varphi_0$ is the position of the peak and $g$ is a gain factor that sets the maximum firing @@ -69,7 +69,7 @@ data, and estimate the orientation angle of the bar from single trial data by the two different methods. - \part Compare, illustrate and discuss the performance of your two + \part Compare, illustrate and discuss the performance of the two decoding methods by using all of the recorded responses (all \texttt{population*.mat} files). How exactly is the orientation of the bar encoded? How robust is the estimate of the orientation